## Abstract

Group comparisons can be conducted at three levels: (1) group means, (2) both group means and variabilities, and (3) group distributions. A traditional contrast is defined as a linear combination of group means; thus, traditional contrast analysis may only effectively address group comparisons in the first level. The concept of a contrast variable has recently been proposed. A contrast variable is defined as a linear combination of random variables (each variable representing random values in a group) instead of group means. Based on a contrast variable, we can use the mean of a contrast to address questions on group comparisons at the first level as in traditional contrast analysis. Meanwhile, we can use the ratio of mean to standard deviation of a contrast variable, that is, standardized mean of a contrast variable (SMCV), to effectively address questions at the second level. We can further use the probability that a contrast variable obtains a positive value, that is, c ^{+}-probability, to effectively address questions at the third level. In this article, we explore the use of contrast variable, SMCV, and c ^{+}-probability for comparing multiple groups in biopharmaceutical studies. Contrast variable, c ^{+}-probability, and SMCV are applicable in a comparison context with or without independence and with or without homoscedasticity.

Original language | English |
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Pages (from-to) | 228-239 |

Number of pages | 12 |

Journal | Statistics in Biopharmaceutical Research |

Volume | 4 |

Issue number | 3 |

DOIs | |

State | Published - Jul 2012 |

## Keywords

- c -probability
- Effect size
- Standardized mean of a contrast variable

## ASJC Scopus subject areas

- Statistics and Probability
- Pharmaceutical Science